Questions: Consider a charge in the presence of a magnetic field. When does it experience a force from that field? (A) Only if the charge is moving (B) Always (C) Only if the charge is not moving (D) Never

Consider a charge in the presence of a magnetic field. When does it experience a force from that field? (A) Only if the charge is moving (B) Always (C) Only if the charge is not moving (D) Never
Transcript text: Consider a charge in the presence of a magnetic field. When does it experience a force from that field? (A) Only if the charge is moving (B) Always (C) Only if the charge is not moving (D) Never
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Solution

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Solution Steps

Step 1: Understanding the Lorentz Force

The force experienced by a charge in a magnetic field is described by the Lorentz force law. According to this law, a charge \( q \) moving with velocity \( \mathbf{v} \) in a magnetic field \( \mathbf{B} \) experiences a force given by:

\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]

Step 2: Analyzing the Conditions for Force

From the Lorentz force equation, it is clear that the force depends on the cross product of the velocity \( \mathbf{v} \) and the magnetic field \( \mathbf{B} \). This implies that:

  • If the charge is not moving (\( \mathbf{v} = 0 \)), the cross product is zero, and thus the force is zero.
  • If the charge is moving (\( \mathbf{v} \neq 0 \)), the cross product is generally non-zero, and the charge experiences a force.
Step 3: Evaluating the Options

Given the conditions derived from the Lorentz force law:

  • (A) Only if the charge is moving: This is correct because a stationary charge (\( \mathbf{v} = 0 \)) does not experience a force.
  • (B) Always: This is incorrect because a stationary charge does not experience a force.
  • (C) Only if the charge is not moving: This is incorrect because a stationary charge does not experience a force.
  • (D) Never: This is incorrect because a moving charge does experience a force.

Final Answer

The correct answer is \(\boxed{\text{A}}\).

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